Combinatorics and Optimization

The Department of Mathematical Sciences has a small active group
with interests in discrete mathematics, matroid theory, combinatorial
optimization, graph theory and probabilistic methods. Each year
the department offers 56 combinatorics and optimization courses
at the junior, senior and graduate levels. These courses cover the
methods, the models, and the theory of discrete optimization, linear
programming and graph theory. An important component in these courses
is the use of technology software such as LINDO. In alternate semesters,
special topics courses in combinatorics and optimization are offered
at the graduate level. Recent topics have included algebraic combinatorics,
matroid theory, and linear algebra methods.
In addition there is a weekly seminar on combinatorics and optimization
 recent topics have included: probabilistic methods in discrete
mathematics, randomized algorithms, discrete geometry and convex
polytopes. Usually two or three distinguished researchers from academia
or industry visit our department each year to give invited lectures
and consult.

Combinatorics and Optimization Faculty

Prof. Mark Kayll,
Ph.D., Rutgers University, 1994
Research interests: discrete mathematics, probabilistic methods,
optimization, theoretical computer science.
Selected publications:
 On the Stochastic Independence Properties of Hardcore Distributions,
Combinatorica 17 (1997), 369391 (with J. Kahn).
 Asymptotics of the total chromatic number for multigraphs,
Australasian Journal of Combinatorics 19 (1999),
279281.
 Asymptotically good choice numbers of multigraphs , Ars
Combinatoria, to appear.
 On pebbling threshold functions for graph sequences (with
Andrzej Czygrinow, Nancy Eaton and Glenn Hurlbert), submitted
for publication.
Prof. Jenny McNulty, Ph.D.,
University of North Carolina at Chapel Hill, 1993 Research interests:
matroid theory, combinatorics. Selected publications:
 Connected Hyperplanes in Binary Matroids, Journal of Combinatorial
Theory, Series B 79 (2000), 8797, (with H. Wu).
 The Matroid Ramsey Number n(6,6), Combinatorics, Probability
& Computing 8 (1999), 229235, (with J. Bonin
and T.J. Reid).
 On Amalgams and Density of Uniform Matroids, Congressus
Numerantium 136 (1999), 193199, (with J. Corp).
 Ports and Oriented Matroids, Congressus Numerantium,
96 (1993), 1120.
Prof. George McRae, Ph.D., University
of Washington, 1967
Research interests: homological algebra, ring theory, category theory,
operations research. Selected publications:
 A Network Model for Determining Trunk Lines with Redundancy,
Ninth Annual Proceedings of American Institute for Decision
Sciences, (1980) 187190. (with Hien Nguyen).
 On Karmarkar's New Projective AlgorithmTheory and Applications
(invited address), Decision Sciences Institute (Phoenix 1986).
Prof. Cory Palmer, Ph.D., Central European University, 2008
Research interests: graph colorings, extremal set systems and applied problems in graph theory.
Other faculty members with interests and backgrounds in probability,
statistics, algebra, analysis, computing and mathematical modeling
often interact with and participate in the combinatorics and optimization
activities of the department.

